Percentages describe a quantity as a part out of 100. They are used for prices, discounts, budgets, grades, business reports, surveys, growth rates and everyday comparisons. Although the arithmetic is usually simple, percentage questions are easy to misread because different problems use different reference values. This guide shows how to find a percentage of a number, determine what percentage one value is of another, calculate percentage increase or decrease, reverse a percentage calculation, and check the result.
What does a percentage mean?
A percentage is a number expressed per hundred. For example, 25% means 25 out of 100, which is the same as 0.25 as a decimal. A percentage can also be greater than 100% when the amount exceeds its reference value.
Formula: find a percentage of a number
Percentage of a number = (Percentage ÷ 100) × NumberFor example, 15% of 240 is (15 ÷ 100) × 240 = 36.
Use Tervilo's Percentage Calculator
For repeated calculations, use the Tervilo Percentage Calculator. It is useful for checking a result quickly or comparing several values without repeating the arithmetic manually.
Formula: find what percentage one number is of another
Percentage = (Part ÷ Whole) × 100If 36 is what percentage of 240, calculate (36 ÷ 240) × 100 = 15%. The order matters because the whole is the reference denominator.
Formula: percentage increase
Percentage increase = ((New value − Original value) ÷ Original value) × 100If a monthly cost rises from 80 to 92, the increase is 12. Dividing 12 by 80 and multiplying by 100 gives a 15% increase.
Formula: percentage decrease
Percentage decrease = ((Original value − New value) ÷ Original value) × 100If a price falls from 150 to 120, the reduction is 30. Dividing 30 by 150 and multiplying by 100 gives a 20% decrease.
Percentage points vs percentage change
If a rate changes from 20% to 25%, it increased by 5 percentage points. Its relative increase is 25% because the five-point change is divided by the original 20%. These two descriptions are not interchangeable.
Convert decimals, fractions and percentages
Multiply a decimal by 100 to turn it into a percentage. For example, 0.375 becomes 37.5%. Divide a percentage by 100 to turn it into a decimal. To convert 3/8 to a percentage, calculate 3 ÷ 8 × 100 = 37.5%.
Example: a service fee
If a service costs 200 and the fee is 8%, the fee is 16 because 0.08 × 200 = 16. The total is 216 if the fee is added to that same base. Always confirm what amount the percentage is applied to.
Example: budget allocation
If 18,000 of a 60,000 budget is assigned to equipment, the equipment share is (18,000 ÷ 60,000) × 100 = 30%. This is a “what percentage of the whole?” problem.
Example: business growth
A team handles 1,200 requests in one month and 1,500 in the next. The increase is 300. Divide 300 by the original 1,200 and multiply by 100 to get a 25% increase.
Reverse percentage calculations
If 40 is 20% of an unknown number, divide 40 by 0.20 to get 200. If a value increased by 15% and ended at 230, divide 230 by 1.15 to recover the original 200. Reverse calculations use a different relationship from simply finding a percentage of a known number.
Why equal increases and decreases do not cancel
Increasing 100 by 20% gives 120. Decreasing 120 by 20% removes 24 and leaves 96. The second 20% is calculated from 120, not the original 100, so equal percentage changes do not necessarily return to the starting value.
Choose the correct reference value
Many percentage mistakes come from using the wrong denominator rather than from doing the arithmetic incorrectly. Identify whether the base is an original price, total budget, previous period, total population or another defined whole before calculating.
Rounding percentage results
Keep extra precision during the calculation and round the final answer unless the task specifically requires earlier rounding. Repeated early rounding can create small differences in later results.
Percentages in spreadsheets
Spreadsheet percentage formatting represents a decimal value. Entering 15% corresponds to 0.15, so multiplying by a number applies the 15% rate. If a result is unexpectedly 100 times too large or too small, check both the formula and the cell format.
How to check a percentage result
Use a reverse calculation. If 15% of 240 is 36, verify that 36 ÷ 240 × 100 returns 15%. For an increase or decrease, divide the change by the original value. A reverse check catches many denominator and sign errors.
Common mistakes
- Using the new value instead of the original reference value.
- Confusing percentage points with percent change.
- Rounding intermediate values too early.
- Assuming an increase and an equal decrease cancel.
- Applying a percentage to the wrong base amount.
Quick verification checklist
- □ I identified the reference value.
- □ I selected the correct formula.
- □ I distinguished percentage points from percentage change.
- □ I kept adequate precision until the end.
- □ I checked the result independently.
Quick answer
For a percentage of a number, multiply the number by the percentage divided by 100. To find what percentage one value is of another, divide the part by the whole and multiply by 100. For percentage increase or decrease, divide the change by the original value and multiply by 100.
Additional worked percentage examples
Example: Find 20% of 500
Convert 20% to 0.20 and multiply by 500. The result is 100. Therefore, 20% of 500 is 100.
Example: What percentage is 52 of 500?
Divide 52 by 500 and multiply by 100: (52 ÷ 500) × 100 = 10.4%. Therefore, 52 is 10.4% of 500.
Example: Increase from ₹500 to ₹600
The increase is ₹100. Divide ₹100 by the original ₹500 and multiply by 100. The percentage increase is 20%.
Example: Decrease from ₹500 to ₹450
The decrease is ₹50. Divide ₹50 by the original ₹500 and multiply by 100. The percentage decrease is 10%.